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Raise the Roof

Introduction

Raise the Roof is a blackjack side bet that wins if the dealer busts, according to what the dealer's bust card was. The lower the card, the more it pays. Plus, the player has the opportunity to raise his side bet after seeing the dealer's up card.

As of this writing (June 13, 2017), Raise the Roof can be found at the Tortoise Rock in California and unknown casinos in the Czech Republic.

Rules

The game is based on conventional blackjack rules, which I assume the reader understands.

The only rules affecting the Raise the Roof side bet are the number of decks, whether the dealer hits or stands on a soft 17, and the pay table used.

At the time of making his blackjack wager, the player has the option to make the Raise the Roof side bet.

The dealer shall then deal each player two cards and two to himself -- one up and one down, as usual.

If the dealer has blackjack, the Raise the Roof bet shall lose.

Otherwise, if the dealer doesn't have blackjack, the player may raise his Raise the Roof with an additional amount of 1x to 5x the original Raise the Roof wager.

Next, the players shall play out their blackjack hands, as normal. If the player busts, any Raise the Roof wagers will still remain live.

The dealer will then play out his hand. If the dealer has a total of 17 to 21, then all Raise the Roof wagers, both initial and raises, will lose.

If the dealer busts, and the player did not raise his Raise the Roof bet, then the original Raise the Roof wager shall pay 1 to 1.

If the dealer busts, and the player did raise his Raise the Roof bet, then the original Raise the Roof wager and the Raise bet shall pay according to one of the pay tables below, depending on which one management decides to use.

The wins for a 4-5-6-7 refer to the entire dealer hand. The cards do not have to be in that order but there can not be any additional cards. For example, 4-5-6-A-7 would not qualify because of the ace.

There are six pay tables available to casino management for use on the Raise the Roof side bet, as shown in the table below. Pay tables 1 and 2 are meant for six- and eight-deck games where the dealer hits a soft 17. Pay tables 3 and 4 are meant for six- and eight-deck games where the dealer stands on a soft 17. Pay tables 5 and 6 were meant for two-deck games where the dealer hits a soft 17. All wins are on a "to one" basis.

Raise the Roof Pay Tables

Event

Pay Table 1

Pay Table 2

Pay Table 3

Pay Table 4

Pay Table 5

Pay Table 6

4-5-6-7 suited

200

500

200

500

300

500

4-5-6-7

40

50

50

40

30

25

Bust with 6

10

10

10

10

10

10

Bust with 7

5

4

5

5

5

5

Bust with 8

2

2

2

2

2

2

Bust with 9

1

1

1

1

1

1

Bust with 10

1

1

1

1

1

1

Analysis

To analyze this side bet I first had to calculate the probability probability of all possible outcomes of the dealer's hand. The following three tables are more information than you need to know to analyze this side bet, but you never know who will find it useful (including me later on). These tables are "pre-peek," mean before dealer checks for blackjack.

The following table is for the raw dealer probabilities for two decks and the dealer hits a soft 17.

The following table is for the raw dealer probabilities for six decks and the dealer hits a soft 17.

The next three post-peek tables refine the ones above to just the pertinent events for the Raise the Raise side bet and assuming the dealer has already checked for blackjack. These probabilities are important to calculating the expected value of whether to make a small raise (1x), big raise (5x), or no raise.

The next six tables show the expected return for each viable action by dealer up card for the six pay tables above. The only viable plays are:

S = Stand

1x = Make raise bet equal to 1x the Raise the Roof wager.

5x = Make raise bet equal to 5x the Raise the Roof wager.

Pay Table 1 Return — Six Decks — Dealer Hits on Soft 17Expand

Ace up

No Raise

1x Raise

5x Raise

Max EV

Strategy

Prob.

Return

A

-0.597439

-0.929011

-2.787033

-0.597439

S

0.053178

-0.031771

2

-0.286680

-0.189436

-0.568308

-0.189436

1x

0.076923

-0.014572

3

-0.246084

-0.122798

-0.368394

-0.122798

1x

0.076923

-0.009446

4

-0.203060

0.125153

0.375458

0.375458

5x

0.076923

0.028881

5

-0.160736

0.367243

1.101728

1.101728

5x

0.076923

0.084748

6

-0.121480

0.738589

2.215768

2.215768

5x

0.076923

0.170444

7

-0.476128

-0.508589

-1.525766

-0.476128

S

0.076923

-0.036625

8

-0.512613

-0.675582

-2.026746

-0.512613

S

0.076923

-0.039432

9

-0.541516

-0.747218

-2.241654

-0.541516

S

0.076923

-0.041655

10

-0.539523

-0.744198

-2.232593

-0.539523

S

0.283948

-0.153196

Blackjack

-1.000000

0.047489

-0.047489

Total

1.000000

-0.090113

Pay Table 2 Return — Six Decks — Dealer Hits on Soft 17Expand

Ace up

No Raise

1x Raise

5x Raise

Max EV

Strategy

Prob.

Return

A

-0.597439

-0.955743

-2.867228

-0.597439

S

0.053178

-0.031771

2

-0.286680

-0.227708

-0.683124

-0.227708

1x

0.076923

-0.017516

3

-0.246084

-0.159614

-0.478842

-0.159614

1x

0.076923

-0.012278

4

-0.203060

0.145095

0.435285

0.435285

5x

0.076923

0.033483

5

-0.160736

0.347231

1.041693

1.041693

5x

0.076923

0.080130

6

-0.121480

0.687412

2.062235

2.062235

5x

0.076923

0.158633

7

-0.476128

-0.517268

-1.551805

-0.476128

S

0.076923

-0.036625

8

-0.512613

-0.710366

-2.131098

-0.512613

S

0.076923

-0.039432

9

-0.541516

-0.780134

-2.340402

-0.541516

S

0.076923

-0.041655

10

-0.539523

-0.777803

-2.333409

-0.539523

S

0.283948

-0.153196

Blackjack

-1.000000

0.047489

-0.047489

Total

1.000000

-0.107715

Pay Table 3 Return — Six Decks — Dealer Stands on Soft 17Expand

Ace up

No Raise

1x Raise

5x Raise

Max EV

Strategy

Prob.

Return

A

-0.665935

-1.115646

-3.346937

-0.665935

S

0.053178

-0.035413

2

-0.292994

-0.206674

-0.620022

-0.206674

1x

0.076923

-0.015898

3

-0.251612

-0.137880

-0.413640

-0.137880

1x

0.076923

-0.010606

4

-0.208392

0.147135

0.441406

0.441406

5x

0.076923

0.033954

5

-0.163187

0.397087

1.191262

1.191262

5x

0.076923

0.091636

6

-0.154317

0.667471

2.002412

2.002412

5x

0.076923

0.154032

7

-0.476128

-0.490317

-1.470952

-0.476128

S

0.076923

-0.036625

8

-0.512613

-0.675582

-2.026746

-0.512613

S

0.076923

-0.039432

9

-0.541516

-0.747218

-2.241654

-0.541516

S

0.076923

-0.041655

10

-0.539523

-0.744198

-2.232593

-0.539523

S

0.283948

-0.153196

Blackjack

-1.000000

0.047489

-0.047489

Total

1.000000

-0.100694

Pay Table 4 Return — Six Decks — Dealer Stands on Soft 17Expand

Ace up

No Raise

1x Raise

5x Raise

Max EV

Strategy

Prob.

Return

A

-0.665935

-1.115646

-3.346937

-0.665935

S

0.053178

-0.035413

2

-0.292994

-0.206674

-0.620022

-0.206674

1x

0.076923

-0.015898

3

-0.251612

-0.137880

-0.413640

-0.137880

1x

0.076923

-0.010606

4

-0.208392

0.127994

0.383982

0.383982

5x

0.076923

0.029537

5

-0.163187

0.377946

1.133838

1.133838

5x

0.076923

0.087218

6

-0.154317

0.657900

1.973700

1.973700

5x

0.076923

0.151823

7

-0.476128

-0.499888

-1.499664

-0.476128

S

0.076923

-0.036625

8

-0.512613

-0.675582

-2.026746

-0.512613

S

0.076923

-0.039432

9

-0.541516

-0.747218

-2.241654

-0.541516

S

0.076923

-0.041655

10

-0.539523

-0.744198

-2.232593

-0.539523

S

0.283948

-0.153196

Blackjack

-1.000000

0.047489

-0.047489

Total

1.000000

-0.111737

Pay Table 5 Return — Two Decks — Dealer Hits on Soft 17Expand

Ace up

No Raise

1x Raise

5x Raise

Max EV

Strategy

Prob.

Return

A

-0.594889

-0.920284

-2.760851

-0.594889

S

0.053025

-0.031544

2

-0.286945

-0.189126

-0.567378

-0.189126

1x

0.076923

-0.014548

3

-0.245079

-0.125386

-0.376158

-0.125386

1x

0.076923

-0.009645

4

-0.197343

0.112732

0.338195

0.338195

5x

0.076923

0.026015

5

-0.152664

0.364340

1.093019

1.093019

5x

0.076923

0.084078

6

-0.122492

0.690583

2.071749

2.071749

5x

0.076923

0.159365

7

-0.477714

-0.535973

-1.607919

-0.477714

S

0.076923

-0.036747

8

-0.516741

-0.701392

-2.104176

-0.516741

S

0.076923

-0.039749

9

-0.538203

-0.737630

-2.212890

-0.538203

S

0.076923

-0.041400

10

-0.537711

-0.743714

-2.231143

-0.537711

S

0.283794

-0.152599

Blackjack

-1.000000

0.047797

-0.047797

Total

1.000000

-0.104571

Pay Table 6 Return — Two Decks — Dealer Hits on Soft 17Expand

Ace up

No Raise

1x Raise

5x Raise

Max EV

Strategy

Prob.

Return

A

-0.594889

-0.920284

-2.760851

-0.594889

S

0.053025

-0.031544

2

-0.286945

-0.189126

-0.567378

-0.189126

1x

0.076923

-0.014548

3

-0.245079

-0.125386

-0.376158

-0.125386

1x

0.076923

-0.009645

4

-0.197343

0.105796

0.317387

0.317387

5x

0.076923

0.024414

5

-0.152664

0.357404

1.072211

1.072211

5x

0.076923

0.082478

6

-0.122492

0.687115

2.061344

2.061344

5x

0.076923

0.158565

7

-0.477714

-0.539441

-1.618324

-0.477714

S

0.076923

-0.036747

8

-0.516741

-0.701392

-2.104176

-0.516741

S

0.076923

-0.039749

9

-0.538203

-0.737630

-2.212890

-0.538203

S

0.076923

-0.041400

10

-0.537711

-0.743714

-2.231143

-0.537711

S

0.283794

-0.152599

Blackjack

-1.000000

0.047797

-0.047797

Total

1.000000

-0.108573

The next table summarizes the house edge and Element of Risk under all six sets of rules. As a reminder, the house edge is the ratio of the expected player loss to initial bet and the Element of Risk is the ratio of the expected player loss to the total average bet (including raises).

House Edge Summary

Decks

Soft 17

Pay Table

House Edge

Element of Risk

6

Hit

1-1-2-5-10-40-200

9.01%

3.90%

6

Hit

1-1-2-4-10-50-500

10.77%

4.67%

6

Stand

1-1-2-5-10-50-200

10.07%

4.36%

6

Stand

1-1-2-5-10-40-500

11.17%

4.84%

2

Hit

1-1-2-5-10-30-300

10.46%

4.53%

2

Hit

1-1-2-5-10-25-500

10.86%

4.70%

Strategy

The strategy nicely works out the same for all pay tables and sets of rules. The following table shows the mathematically best action for every dealer up card. Here, again, are the abbreviations for the strategy: S=Stand, 1x= 1x Raise, 5x=5x raise.